How Do Natural Frequencies Arise in a Clamped Metal Rod?

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Homework Statement



A thin, flexible metal rod has a length of 0.606 meters. One end of the rod is clamped to a table, and the other end can vibrate freely. What are the first three natural frequencies of the rod if the wave speed in the rod is 27.4 meters per second? Hint: Draw pictures of what the rod will look like when it is vibrating at the first three harmonics.

The Attempt at a Solution



How would the open end affect the motion? I am confused here...
 
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